Design and simulation of wind energy conversion system commanded by converter and mechanical brake

Abstract

This paper concern the design and control of a wind energy conversion system regulating generator phase’s currents, voltages, and batteries charging voltage using barking systems and AC–DC converter. Indeed, the braking system permit the regulation of the generator’s angular speed and electromotives forces magnitude, and the AC–DC converter permit the regulation of the phase’s voltages, currents, and the batteries charging voltage. This method is suitable for permanent magnet axial ﬂux synchronous generators and for Insulated Gate Bipolar Transistor converters (IGBT). In addition, we propose an innovative strategy to push the problem of adding an impedance matching transformer to minimize the over-current effect caused by the sudden variation of the voltage at the generator inductor using the AC–DC converter. It offers the advantage of power chain cost reduction and the improvement of its performances. The overall model of the power chain is implemented under the simulation environment MATLAB-Sumilink for performances analysis of studied structure.

Keywords

Wind turbine design control permanent magnets generator PWM AC–DC converter braking system

Introduction

Wind energy conversion chains recharging batteries using a PD3 rectifier have the disadvantage of serious over-voltages at the generator inductances due to spontaneous switching of the rectifier power diodes ( Tounsi, 2022a ). These over-voltages depend on the value of the equivalent inductance of generator phase [1 and 2]. This problem is classically solved by the user of a transformer which is in most cases expensive. For this study, this problem is solved by using an AC–DC converter regulating the voltages and phase currents of the generator as well as the battery recharge voltage to their optimal values defined by the analytical design model of the generator.

A mechanical braking system is used to regulate the angular velocity of the wind turbine to its nominal value defined by the analytical design model. This braking system regulates the magnitude of the electromotive forces to its nominal value.

Other problems are posed during the design of the components of the power chain of wind turbines such as the problem of performance optimization and the cost of the study (Tounsi, 2021a, 2021b, 2022b).

These problems are solved by the choice of the analytical design method given its good integration with high-dimensional stochastic optimization methods and its simplicity (Amor et al., 2015; Nath and Rana, 2011; Neji et al., 2006; Nhidi et al., 2015; Qiu et al., 2011; Thongam et al., 2009; Tounsi, 2015a, 2015b, 2022b).

In this context, this paper is organized as follows.

Introduction.

Power chain components and structure.

Power chain model.

Simulation results.

Conclusion.

Operation principle

The choice of the components of the energy generation chain is a decisive factor determining the cost of production and the profitability of the production chain. As a result, our chain comprises an horizontal axis propeller transferring the kinetic energy of the air in motion by means of a speed multiplier to the synchronous generator. The latter makes it possible to induce three three-phase sinusoidal electromotive forces proportional to the speed at the motor shaft. These three electromotive forces will be converted through a pulse width modulation converter. The output voltage of the converter is applied directly to the terminals of the batteries to store the transferred energy.

In fact, when the wind speed is high, the maximum value of the electromotive forces is important. Thus, the current in the generator-rectifier-battery is important, so the system must be monitored to protect the power chain from burning and an electromagnet braking system is used to reduce the speed of the generator shaft in order to ensure a continuous charging with a maximum current equal to 2600 A.

Today, the only commercial wind turbines are horizontal. This type of wind turbine has gained the upper hand over those with a vertical axis because they represent a lower cost, they are less exposed to mechanical stresses, the position of the receiver at several tens of meters of the ground favors the efficiency and the three-bladed rotor constitutes a compromise between the power coefficient, the cost and the speed of rotation of the wind sensor. So for these reasons our choice is focused on the three-bladed propeller with horizontal axis (Tounsi, 2021a, 2021b, 2022a, 2022b).

Generator design

The generator choice was based on a modular structure of permanent magnet synchronous generators (PMAFSG), since this structure makes it possible to stack up to increase the generated power and makes it possible to attain important values of currents in view that the magnetic reaction is reduced by the magnetic effect of the magnets. Moreover, this structure is at reduced cost of production, since it has a straight and open slots which is easy to make, the winding is concentrated, which allows them to be inserted in a single block. For designing the electric generator, we chose the analytical method since it presents the following advantages (Tounsi, 2021a, 2021b, 2022a, 2022b):

It produces solutions quickly and without iterations.

It provides acceptable precisions of the results as it is based on simplified assumptions well-argued and suitable for solving a design problem of an electrical device.

It leads to highly configurable design models leading to optimized performance.

This method is adjusted, completed, and validated by finite element simulations.

Figure 1 shows the studied structure of the permanent magnet synchronous generator.

Figure 1.

The permanent magnet axial ﬂux synchronous generator structure.

Converter choice

There are several converter structures used such as the structure which used a diode bridge and a thyristor bridge as well as the structure which consists in replacing the natural switching inverters composed of thyristors by forced switching inverters (Tounsi, 2021a, 2021b, 2022a, 2022b).

Our choice was based on a robust two-level pulse width modulation (PWM) converter structure to overcome the overvoltage and overcurrent problem caused by the natural disconnection of a generator phase caused by the current inertia effect caused by the sudden change from a large current value to a much lower value due essentially to the presence of an inductance at the terminals of each phase of the generator. When a rectifier PD3 is used, to remedy this problem, an impedance matching transformer is used whose secondary has a negligible inductance. Our solution allows pushing the problem of overcurrent without adding a transformer. It allows a significant gain in the cost of the power chain. The structure of the converter is given in Figure 2.

Figure 2.

Schema of the pulse width modulation converter.

Batteries

The batteries have the role of storing the electricity produced by the wind turbine in particular. They then redistribute it as needed.

The energy accumulator is a connection of elementary battery modules in series and in parallel so as to have a nominal voltage and a power storage capacity defined by the specifications of the studied application. The model of accumulator chosen for this study is the Tevenin model given by Figure 3 (Nhidi et al., 2015; Tounsi, 2015a, 2021a, 2021b, 2022a, 2022b).

Figure 3.

Batteries model.

Conversion chain modeling

Motion equation

The equation governing the motion of the rotating parts of the energy generation chain is deduced from the bellow fundamental relation of dynamics (Tounsi, 2021a, 2021b, 2022a, 2022b).

J \times \frac{d Ω}{dt} = T_{m} - r_{d} \times (T_{em} - sgn (T_{em}) \times T_{mec} - sgn (T_{em}) \times T_{fer}) - T_{c}

(1)

where J is the moment of inertia of the rotating parts, r_d is the speed amplification ratio, T_m is the torque imposed on the motor shaft caused by the movement of wind, T_em is the electromagnetic torque, T_mec is the torque due the mechanical losses, T_fer is the torque due to iron losses, and T_c is the braking torque.

The different torques are expressed by the following equations:

T_{m} = \frac{1.918 \times R_{p}^{2} \times V_{vent}^{3}}{Ω}

(2)

where 1.918 is a coefficient that depends on the kinetic energy of the wind and pale properties, R_p is the pale ray, and V_vent is the wind speed.

T_{em} = \frac{1}{Ω} \sum_{i = 1}^{3} e_{i} \times i_{i}

(3)

Where e_i and i_i are, respectively, the induced electromotive force and the current of the phase i.

T_{mec} = s + K \times Ω \times γ + Ω^{2}

(4)

where s is a dry friction coefficient, k is a viscous friction coefficient, γ is a fluid friction coefficient, and Ω is the angular velocity of the electrical generator.

T _c is the braking torque given as the output of the brake system block.

The model of the motion equation is implemented in Simulink according to Figure 4.

Figure 4.

Simulink model of the motion equation.

Induced electromotive forces

The Simulink model of induced electromotive forces is illustrated in Figure 5 (Tounsi, 2015a, 2021a, 2021b, 2022a, 2022b).

Figure 5.

Simulink model of the induced electromotive forces.

The three induced electromotive forces are estimated from the following three equations:

E_{a 1} = \frac{2}{3} \times K_{e} \times Ω \times \cos (p \times Ω \times t + \frac{π}{2})

(5)

E_{a 2} = \frac{2}{3} \times K_{e} \times Ω \times \cos (p \times Ω \times t - \frac{2 \times π}{3} + \frac{π}{2})

(6)

E_{a 3} = \frac{2}{3} \times K_{e} \times Ω \times \cos (p \times Ω \times t - \frac{4 \times π}{3} + \frac{π}{2})

(7)

where K_e is the electromotive constant, Ω is the angular velocity of the generator, and p is the number of pole pairs.

The three generator’s constants E₁, E₂, and E₃ are estimated by the following three equations:

E_{1} = \frac{E_{a 1}}{Ω}

(8)

E_{2} = \frac{E_{a 2}}{Ω}

(9)

E_{3} = \frac{E a_{3}}{Ω}

(10)

Electrical generator

Each phase of the generator is equivalent to a resistor in series with an inductance and a back electromotive force. The model of the three phases is described by the following equations (Nhidi et al., 2015; Tounsi, 2015a, 2021a, 2021b, 2022a, 2022b).

v_{1} = R \times i_{1} + (L - M) \times \frac{d i_{1}}{dt} + e_{1}

(11)

v_{2} = R \times i_{2} + (L - M) \times \frac{d i_{2}}{dt} + e_{2}

(12)

v_{3} = R \times i_{3} + (L - M) \times \frac{d i_{3}}{dt} + e_{3}

(13)

where R, L, and M are, respectively, the resistance, the inductance, and the mutual inductance of the motor, i_i, u_i, and e_i are, respectively, the current, the voltage, and the induced electromotive force of the phase i.

These equations are implemented under MATLAB-Simulink according to Figure 6.

Figure 6.

Simulink model of the electrical generator.

Static converter

A three-phase IGBT bridge converter controlled by a control signals generator is used. Its Simulink model is given in Figure 7 (Nhidi et al., 2015; Tounsi, 2015a, 2021a, 2021b, 2022a, 2022b).

Figure 7.

Simulink model of the converter.

Control signals generator

The control signals generator compares the three reference voltages calculated by the current regulator to a higher frequency triangular signal. The Simulink model of the control signal generator is illustrated in Figure 8 (Tounsi, 2015a, 2021a, 2021b, 2022a, 2022b).

Figure 8.

Simulink model of the control signals generator.

The output of each comparator affects alternatively an hysteresis varying between “1” and “0” to produce the switch control signals of the switches S₁, S₂, S₃, S₄, S₅, and S₆. To avoid short circuits, the control pulses S₁, S₃, and S₅ are shortened to avoid overlapping between two control signals of an arm. The current regulator adjusts and fine-tunes the pulse width of the control signals so as to impose the currents in phase with the induced electromotive forces in order to maximize the recovered energy.

Currents regulator

Currents regulator allow the imposition of currents having the same shape and in phase with the induced electromotive forces in order to maximize the recovered energy. Figure 9 presents the Simulink model of currents regulator (Tounsi, 2015a).

Figure 9.

Simulink model of the currents regulator.

Indeed, the reference currents are compared to the generator phase currents. The outputs of the three comparators attacks three regulators proportional/integral type (PI) to provide the three ideal reference voltages necessary to impose currents in phase with the induced electromotive forces in order to maximize recovered energy.

Accumulator model

The accumulator model chosen for this study is illustrated in Figure 10 (Nhidi et al., 2015; Tounsi, 2015a, 2021a, 2021b, 2022a, 2022b).

Figure 10.

Simulink model of the batteries.

where R₁ and C₁ are the resistance and the capacity taking into account the transitional arrangements.

R_i is the internal resistance of the battery.

Model of the all generator-converter-batteries

The Simulink model of the generator-converter-batteries assembly is shown in Figure 11.

Figure 11.

Simulink model of the generator-converter-batteries assembly.

Batteries load current regulator

The batteries current regulator (Figure 12) limits the batteries charging current to a value equal to 2600 A, to protect the energy generation chain against the burn via an integral proportional regulator producing the control signal of the electro magnet. This value is held into account by the design approach of the generation chain

Figure 12.

Simulink model of the braking torque regulator.

Generation chain global model

The coupling of different models of the generation chain leads the global model implanted under the environment of MATLAB-Simulink according to Figure 13.

Figure 13.

Simulink model of the global wind energy generation chain.

Simulation results and discussion

Simulation parameters (Table 1) are calculated from a generator designing and sizing model.

Table 1.

Simulation parameters.

Nomenclatures	Values	Units
Phase resistance (R)	0.241	mΩ
Phase inductance (L)	0.00676579136	mH
Mutual inductance (M)	0.00440625320	mH
Moment of inertia of the rotating parts (J)	25,278.775	kg m²
Internal resistance of the battery (R_i)	0.1	Ω
Resistance modeling the transitional arrangements for charging and discharging of batteries indentified by experimental test (R₁)	0.01	Ω
Capacity modeling the transitional arrangements for charging and discharging of batteries indentified by experimental test (C₁)	1	Farad
Gear ratio (r_d)	1	/
Batteries nominal voltage (U_dc)	2.4	Volt

Figure 14 illustrates the evolution of wind speed over time. This speed cycle has high accelerations and critical values to test the performance of the studied braking system.

Figure 14.

Wind speed profile.

Figure 15 illustrates he angular velocity of the generator shaft. Figure 15 shows that after training in movement of the generator shaft, the wind stopping does not immediately causes the stop of the generator shaft as a result of the inertia of the rotating parts. In this case and for this structure, the speed is maintained constant when the charging current of the battery is reduced by the regulation of the current.

Figure 15.

The angular velocity of the generator shaft.

The amplitude of the electromotive forces illustrated in Figure 16 is relatively high, which is explained by the insertion of a gear amplifier with amplifying ratio r_d. This is to compensate the drop of phase voltages of the generator at battery charging phase. The magnitude of the electromotive forces is regulated by the braking system to its optimal value.

Figure 16.

Induced electromotive forces: (a) volution of the induced electromotive forces and (b) zoom of the evolution of the induced electromotive forces.

Figure 17 shows the evolution of the generator phase’s voltages. Their amplitude is reduced compared to the amplitude of the electromotive forces since the voltage drop at the phase resistors is high. The slight deformation in the forms of the voltages is mainly due to the presence of the inertia effect in current of the phase inductances. The magnitude of the phase’s voltages is regulated by the AC–DC converter.

Figure 17.

Generator phases voltages: (a) evolution of the generator phases voltages and (b) zoom of the evolution of the generator phases voltages.

The evolution of the generator phase’s currents is illustrated in Figure 18. The slight deformation is due to the forced connection to the batteries of one phase instead of another. The magnitude of the phase’s currents is regulated by the AC–DC converter and the braking system. The AC–DC converter permit the protection wind turbine against over voltage.

Figure 18.

Generator phases currents: (a) evolution of the generator phases currents and (b) zoom of the evolution of the generator phases currents.

Figure 19 shows that the recharging current is regulated at optimal continuous value equal to 2600 A. This property confirms the efficiency of the developed control algorithm. The change in the time of this current allows a continuous recharge of the batteries.

Figure 19.

Batteries charging current.

Figure 20 shows that the braking torque is high for high-speed values, which is explained by the fact that the recharging of the current battery has exceeded the limit set at 2600 A. Indeed, braking torque is with high value pending wind high speed.

Figure 20.

Evolution of the braking torque.

Figure 21 shows that this power chain provides continuous energy recovery at optimal regime.

Figure 21.

Evolution of the recovered power.

Conclusion

This paper concern the design and control of wind turbine power chain using braking system and AC–DC converter. The braking system permit the regulation of the generator’s angular speed and electromotives forces magnitude. The AC–DC converter permit the regulation of the phase’s voltages, currents, and the batteries charging voltage. This method is suitable for permanent magnet axial ﬂux synchronous generators and for Insulated Gate Bipolar Transistor converters (IGBT). This study valid the innovative control strategy to push the problem of adding an impedance matching transformer to minimize the over-current effect caused by the sudden variation of the voltage at the generator inductor using the AC–DC converter. It offers the advantage of power chain cost reduction and the improvement of its performances. The overall model of the power chain is implemented under the simulation environment Matlab-Sumilink for performances analysis of studied structure.

Simulation results are encouraging and validate completely the design and control approach of the generation of renewable energy chain.

Footnotes

Declaration of conflicting interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Souhir Tounsi

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